Could you please help
prove the expansion. cos x = 1 - x^2/2! + x^4/4! - x^6/6! ..... + (-1)^n x^2n/(2n)! + .....
Thank You
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Could you please help
prove the expansion. cos x = 1 - x^2/2! + x^4/4! - x^6/6! ..... + (-1)^n x^2n/(2n)! + .....
Thank You
The MacLaurin series for f(x) is:Quote:
Originally Posted by grabick_luca
f(x) = f(0) + f'(0) x /1! + f''(0) x^2 /2! + .... f^(n) x^n /n! + ...
Now D^(2n) cos(x) = (-1)^n cos(x), and D^(2n-1) cos(x) = (-1)^n sin(x).
and the result follows.
RonL
Hello, grabick_luca!
Quote:
Prove the expansion:
. . cos x .= .1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ... + (-1)^n (x^{2n})/(2n)! + .....
Are you supposed to derive the expansion by the Maclaurin procedure?
If you know the procedure, what's stopping you?